You have to center every thing becuse you need to start somewhere, you have to have a base line to adjust aginst. You cant just have everthing willy nilly and start makeing adjustments here and there, got to start in the middle.Yes you will need to trim for more right than left it will turn left on its own the tourqe will do that for you. You have to fight the tourqe to turn right so you will need more throw that way. And no you cant adjust anything above the swashplate that will effect cyclic only collective. It matters not that the swashplate is not level only that the heli lifts off level.
Do the same adjusting that you are doing on the main rotor to the tail rotor. Find the spot where it(the heli) stays stright and adjust the linkage so the tail rotor stays there after you put the trim in the center.